Remodeling in response to functional requirements is the phenomenon which makes living structural materials different -- and more efficient -- than other structural solids. The principal concern of the research proposed here is the functional adaption of mature bone in response to its strain history and distribution. This adaptation is manifested as changes in the cross-sectional geometry of long bones, and as changes on the structural material properties of the bone. Of particular interest is the development of a theoretical framework for bone remodeling, and an associated computational method to establish a predictive computational tool which will be of general utility for determining the consequences of various theories for strain-induced bone remodeling. This theoretical work and the development of a computational vehicle for testing theoretical consequences may also help suggest priorities for experiments designed to stimulate strain-induced bone remodeling. Once reasonable theories and their associated constants can be tested experimentally, the models can be used to predict the consequences to bone architecture resulting from orthopaedic implants. In this way, more rational and successful methods for the design of orthopaedic implants can be expected. It is anticipated that this approach to implant design will produce a less expensive method than design by clinical trial alone. Future research, based in part on the work proposed here, may also eventually help guide physicians in recommending specific activities to help reduce the chances for implant failure.